Vehicle minimization for periodic deliveries

We consider the problem of minimizing the number of vehicles required to make strictly periodic, single destination deliveries to a set of customers, under the initial assumption that each delivery requires the use of a vehicle for a full day. This problem is motivated by inventory routing problems in which customers consume goods at a steady rate. We evaluate the complexity of the problem and discuss its general properties, including problem decomposition. We also present an algorithm that we show is optimal for special cases. Finally, we extend these results to a general version of the problem.